Bayesian hierarchical modeling for integrating low-accuracy and high-accuracy experiments

Standard practice in analyzing data from different types of ex-periments is to treat data from each type separately. By borrowing strength across multiple sources, an integrated analysis can produce better results. Careful adjustments need to be made to incorporate the systematic differences among various experiments. To this end, some Bayesian hierarchical Gaussian process models (BHGP) are pro-posed. The heterogeneity among different sources is accounted for by performing flexible location and scale adjustments. The approach tends to produce prediction closer to that from the high-accuracy ex-periment. The Bayesian computations are aided by the use of Markov chain Monte Carlo and Sample Average Approximation algorithms. The proposed method is illustrated with two examples: one with de-tailed and approximate finite elements simulations for mechanical ma-terial design and the other with physical and computer experiments. KEY WORDS: computer experiments; kriging; Gaussian process; de-sign of experiments